Ph.D. (Doctor of Philosophy)
Department of Psychology
Analysis of covariance; Regression analysis
Violations of the multivariate normality assumption in covariance structure modeling (CSM) procedures are a common occurrence that can substantially impact the statistical and practical implications of research results. Numerous potential remedies for the impact of nonnormality on CSM have been suggested, including different estimation methods and robust calculations of test statistics and parameter estimates; however, each have their limitations and drawbacks. An additional remedy termed bootstrapping has been long advocated as an adequate means to minimize the effects of nonnormality; however, there have been no large-scale simulation studies aimed at exploring bootstrapping's actual utility. The present study employed Monte Carlo simulation and model-based bootstrapping methods to investigate the impact of sample size and data nonnormality on several CSM fit statistics and indices, parameter estimation bias, and parameter standard error bias. The specified model and population matrix were from a well-studied model of alienation that has been used in previous simulation research. The results found that bootstrapping mitigated the impact of larger sample sizes and moderate nonnormality on three chi-square test statistics but resulted in fit indices that approached their theoretical "ideal" boundaries that could lead to a biased perception of model fit. Bootstrapping did not diminish the impact of nonnormality on parameter estimation biases and actually increased bias in smaller sample sizes. Finally, although bootstrapping did reduce bias in standard error estimates for model variances and covariances, bias for indicator loadings and structural paths increased in the bootstrapped samples. Collectively, the present results suggest that bootstrapping may not be the exceptional remedy for nonnormality as has been suggested by previous writers and several implications of these findings are discussed. Due to the scant amount of research on bootstrapping, however, several directions for future research are presented.
Wilkinson, Wayne W., "A Monte Carlo investigation of bootstrapping in covariance structure modeling under varying levels of multivariate nonnormality" (2008). Graduate Research Theses & Dissertations. 411.
iv, 95 pages
Northern Illinois University
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